From the point of view of a given global agent, a global theory may be represented via a state space \(\Omega \)  and a set of transformations \(\mathcal {T}\)  that are available to the agent
[1]}, [2]}, [3]}, [4]}.
We can think of the state space as the “language” chosen by this global observer to describe nature. For example, \(\Omega \)  could be the set of coordinates and momenta of all celestial bodies; in quantum theory, it could be the set of valid density matrices over a global Hilbert space. It need not be a static picture: in astronomy, an alternative state space \(\Omega ^{\prime }\)  could be the set of possible trajectories of celestial bodies, and in quantum theory it could include all global Hamiltonians that determine the free evolution of density matrices.
Note that
1) \(\Omega \)  is not the ultimate description of reality, just a convenient representation from the point of view of a global agent;
2) different pictures, like \(\Omega \)  and \(\Omega ^{\prime }\) , may be related and mapped to one another [5]}, [6]}; and
3) \(\Omega \)  need not have any special structure a priori besides being a set — indeed, the approach laid out here will allow us to find an operational subsystem structure in the set of states.
